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Search: id:A002262
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| A002262 |
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Integers 0 to n followed by integers 0 to n+1 etc. |
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+0
90
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| 0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5
(list; table; graph; listen)
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OFFSET
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0,6
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COMMENT
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a(n) = n - the largest triangular number <= n. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Dec 25 2001
The PARI functions t1, t2 can be used to read a square array T(n,k) (n >= 0, k >= 0) by antidiagonals downwards: n -> T(t1(n), t2(n)). - Michael Somos, Aug 23, 2002
Values x of unique solution pair (x,y) to equation T(x+y) + x = n, where T(k)=A000217(k). - Lekraj Beedassy (blekraj(AT)yahoo.com), Aug 21 2004
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LINKS
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M. Somos, Sequences used for indexing triangular or square arrays
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FORMULA
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a(n) = (n-((trinv(n)*(trinv(n)-1))/2)); trinv := n -> floor((1+sqrt(1+8*n))/2); # Gives integral inverses of triangular numbers.
a(n)=n-A000217(A003056(n))=n-A057944(n). - Lekraj Beedassy (blekraj(AT)yahoo.com), Aug 21 2004
a(n) = A140129(A023758(n+2)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 14 2008
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MAPLE
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A002262 := n -> n - binomial(floor((1/2)+sqrt(2*(1+n))), 2);
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PROGRAM
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(PARI) a(n)=n-binomial(floor(1/2+sqrt(2+2*n)), 2)
(PARI) t1(n)=n-binomial(floor(1/2+sqrt(2+2*n)), 2) /* A002262 */
(PARI) t2(n)=binomial(floor(3/2+sqrt(2+2*n)), 2)-(n+1) /* A025581 */
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CROSSREFS
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A002260(n)=1+a(n)
Cf. A025675, A025682, A025691, A002024, A048645, A004736, A025581. As a sequence, essentially same as A048151.
Sequence in context: A025690 A025668 A048151 this_sequence A025675 A025682 A025691
Adjacent sequences: A002259 A002260 A002261 this_sequence A002263 A002264 A002265
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KEYWORD
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nonn,tabl,easy,nice
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AUTHOR
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Angele Hamel (amh(AT)maths.soton.ac.uk)
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